In the bowl of a stand mixer fitted with the paddle attachment, cream together the butter and sugar on medium speed until fluffy, about 1 minute. Add the egg and vanilla; beat on low speed to combine. Slowly add the salt and the flour; mix on low speed until just combined.
Roll the dough into 1-inch balls, placing them about 3 inches apart on parchment-lined baking sheets.
Using the back of a rounded teaspoon, press the teaspoon into the top of each cookie, creating a well in the center (make sure not to press all of the way through to the baking sheet itself). Dip the teaspoon in flour or water between each cookie to make this process go a bit easier.
Place the shaped and indented cookies into the refrigerator or freezer to chill for at least 1 hour. Near the end of the chilling time, preheat the oven to 375 degrees and make the filling.
Make the filling:
In a medium bowl, whisk together all of the filling ingredients until well combined. When ready to bake, spoon about 1 teaspoon of filling into each of the indented cookie wells.
Bake cookies for 15-18 minutes, or until cookies are just set and barely golden around the edges. Let cool on the baking sheets for about 5 minutes before moving to a cooling rack to finish cooling.